In theory, it´s possible to calculate an optimum rate of extraction from an ore body, knowledge or precise assumption of the total tonnage and its sequential grades (including the effects of varying the cutoff grade), and of all cost and product prices throughout the project life is required. 💰 The maximized quantity might be total profit, total cash flow, the net present value or the internal rate of return. Thus when allowing for the practical inaccuracies of data, the calculated results cannot be considered critical. Hence, although valid, a highly mathematical approach to mine life determination is seldom of practical use. 🔍 Too low a production rate sacrifices possible economies of scale and defers possible profits too far into the future. Conversely, too high a rate may drive up the project’s capital cost beyond any ability to repay within the shortened life. Too high an output may be unsalable, while too short a life for a large enterprise may be wholly undesirable on social grounds. In real life, rates of output are strongly limited or influenced by practical problems. One of the most important of these is working space. A mine may be able to increase output as it gets older solely because its ever expanding workings offer more points of attack. 🚚 In an open pit the working space for equipment and hence maximum production rate tends to vary with the area (ft2) exposed while tonnage varies with volume (ft3). Thus one might expect the production rate for groups of more-or-less similarly shaped ore bodies to be proportional to the two-thirds power of the ore body tonnage. 🧮 The life would then be proportional to the cube root of that tonnage (F1). In this equation, it is immaterial whether short or metric tons are used. It is more convenient to use quantities expressed in millions and except for special conditions, the practical range of variation seems to lie within a factor of 1.2 above and below (F2). Taylor studied many actual projects (some operating and others only planned) involving a wide range of ore body sizes, and shapes (other than thin deposits of very large lateral extent), for which the total ore reserves were reasonably well known before major design commenced. He found that the extraction rates seemed proportional to the three quarters power of the ore tonnage rather than the two-thirds power. The designed lives were proportional to the fourth root of the tonnage. 💡 The rule provides an appropriate provisional output rate for preliminary economic appraisals and will define a range of rates for comparative valuation at the intermediate stage after which a preferred single rate can be selected for use in the feasibility study. 🖼️ The empirical formula (F2) generates the values presented in table. 📜 Reference: W. Hustrulid, M. Kuchta & R. Martin, Open pit mine planning & design Vol.1 Fundamentals, CRC Press.